How to merge vertices in Blender?
There is a merge tool.
Select the vertices you want to merge.
Press ALTM (or M for Blender 2.8)
There are a few options:
At First, or Last will merge the points depending on the order in which the vertices where selected.
At center. will merge the vertices at the center of all selected vertices.
At cursor will merge the selected vertices where the 3D cursor is.

I recommend you read this page of the blender manual for this and other ways to deal with Deleting and Merging